To address the second need, and relate galaxies to the dark matter haloes in Figure REF ,
we assume for simplicity that the characteristic rotation velocity of a galaxy (which we take to be \(V_{flat}\) )
and that of its host halo at \(R_{200}\)  are equal.
For a massless disc in a [1]} halo, \(V_c\)  at the location of the galaxy can be about half its value at \(R_{200}\) .
However, the self-gravity of the baryons is expected to increase \(V_c\)  in the inner parts of haloes. The amount by which it increases
is difficult to calculate theoretically, so we look to observations. [2]} find a very small conversion factor
between \(V_c\)  at \(R_{200}\)  and at the location of galaxy discs. In their analysis, [2]}
combined dark halo masses measured from satellite kinematics and
weak gravitational lensing to show that \(V_{2.2} \simeq V_{200}\)  for \(V_{2.2} = 90 - 260\)  km s\(^{-1}\) ,
where \(V_{2.2}\)  is the galaxy rotation velocity measured at 2.2 \(I\) -band scale lengths.
This equivalence is also consistent with semi-analytic models of galaxy formation which require a
similar ratio between galaxy and halo velocities to simultaneously match the local Tully-Fisher relation and
galaxy luminosity function [4]}.
